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At least 37 records · Page 2

Application of a Rapid Design Tool to a 3D Woven Structural Joint

The optimization of composite structural joints is an iterative process and a multiscale problem. High fidelity finite element modeling of joints with 3D woven and laminated materials can become computationally expensive. The aim of this paper is to establish a reliable analysis process for the optimization of a composite Y-joint (curved Pi-joint), to be used in an aircraft fuselage, using commercial rapid joint design, analysis, and optimization software. The rapid joint design tool was investigated as a substitute and/or complement to a finite element analysis software. A composite Pi-joint and a composite Y-joint were evaluated using the rapid joint design tool to determine the applicability and limits of the software. Furthermore, three main preliminary parametric studies were performed to better understand the capability of the tool in predicting the stress distributions and trends in the Y-joint. The parameters investigated were the joint curvature, the laminated skin thickness, the adhesive systems, and the ply composition. Lastly, trends in predicted failure load were produced as a function of skin thickness (16ply, 24ply and 32ply). Failure loads were found with varying joint curvature and skin thickness using stress-based adherend failure criterion. The rapid joint design tool was also validated against existing experimental results.

Bonded Joints↗

A simplified all-frequency stable formulation with an implicit Coulomb gauge

A potential-based finite element formulation has been developed in the past to circumvent the low-frequency breakdown issues commonly encountered in electromagnetic (EM) simulations of low-frequency and multiscale problems. In this formulation, the magnetic vector and electric scalar potentials have been employed to express the electric field and magnetic flux, leading to a set of two equations that represents all four Maxwell’s equations and the current continuity equation. To enforce the Coulomb gauge, an auxiliary potential has been introduced, which results in a total of three equations to be solved simultaneously. To reduce the number of equations and unknowns needed in a simulation, a simplified formulation is proposed in this paper to enforce the Coulomb gauge implicitly without the need for the auxiliary potential. A numerical example is given to demonstrate the accuracy of the proposed formulation.

Mekonnen, Minyechil↗

PhILMs: Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems

The landscape of computational science and engineering is continually evolving, with the challenge of high-dimensional regression problems standing as a significant hurdle in numerous scientific endeavors. Addressing this challenge, our research, funded by this award, has led to the development of an innovative computational framework known as Probabilistic Partition of Unity Networks (PPOU-Nets). This initiative represents a collaborative effort to harness the potential of mathematics and physics-informed machine learning in tackling multiscale and multiphysics problems prevalent in high-dimensional spaces. Through this work, we have proposed a novel methodology that seamlessly integrates adaptive dimensionality reduction and a mixture of experts model, thereby facilitating a more efficient and accurate approximation of complex functions. This research effort has not only advanced the state of computational science but also opened new avenues for exploration in quantum computing and beyond. This report outlines the motivation, methodology, key findings, and implications of our work, underscoring our contributions to the broader scientific community and the potential pathways for future research.

97 MATHEMATICS AND COMPUTING↗

Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PHILMS) (Technical Report)

The research work at University of California Santa Barbara (UCSB) resulted in several new developments in the areas of scientific machine learning, numerical analysis, and practical methods for data-driven modeling, prediction, reductions, and simulation. Many of the projects were carried out in collaboration with members of the national laboratories at Sandia National Laboratories (SNL), Pacific Northwestern National Laboratories (PNNL), and other institutions. Results included developing new scientific machine learning methods, related theory and mathematical frameworks for analysis and training, data-driven numerical solvers, and related tools and software for scientific computation. During the support period, over 16+ papers were submitted for publication, and 4 open-source software packages were developed and released (available at http://atzberger.org/). In addition, 7+ students and 2 post-docs were mentored in collaboration with the laboratory staff for future careers in academia, government labs, and industry.

97 MATHEMATICS AND COMPUTING↗

Multiscale Mesh Adaptation for Transonic Aeroelastic Flutter Problems

This work applies multiscale mesh adaptation with refine to reduce spatial discretization error of aeroelastic computational fluid dynamics (CFD) simulations. Benchmark flutter models, such as the pitch and plunge NACA64A-010 airfoil and the benchmark supercritical wing, are studied with both a linearized frequency-domain solver and time-marching CFD coupled to a modal structural solver in FUN3D. The undeformed NASA Common Research Model (CRM), an aeroelastic jig shape variant of the CRM, is also studied with the linearized frequency-domain approach. For these cases, the adaptation process converges to comparable flutter predictions to hand-generated meshes but with smaller node counts. However the additional disciplines of the linearized frequency-domain analysis, the mesh deformation, and the unsteady finite-volume solver create robustness challenges that need to be addressed before it can be applied as a fully automated process for complex transonic aeroelastic problems. In particular, negative volumes are observed to be an issue for FUN3D’s linear elasticity mesh deformation solver when moving the adapted meshes.

Aeroelasticity↗

An integrated coupling model for solving multiscale fluid-fluid coupling problems in SAM code

In this study, an integrated coupling method has been developed for solving multiscale fluid-fluid coupling problems in plant-scale safety analysis models in SAM (System Analysis Module) code. In this method, a higher-fidelity multi-dimensional (3D) flow module is used for reactor components of complex flow features (e.g., reactor core) and a lumped parameter one-dimensional (1D) flow module for plant-scale flow loops (e.g., primary loop pipe network), respectively. In this method, the 3D fluid equation/domain and 1D fluid equation/domain are tightly coupled at the residual level and solved simultaneously using the Newton’s method to overcome the convergence issues typically seen in existing approaches like separate domain approach, where the 3D fluid equation and 1D fluid equation are solved separately. Extensive and successful code verifications and demonstrations have been performed for this newly developed method. This new modeling approach significantly simplify the work flow in developing high-fidelity plant-scale safety analysis model, e.g. for pool-type reactors and pebble-bed reactors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers

Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multispecies problems. An anisotropic relaxation verification test that agrees well with previously published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. Finally, the entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.

97 MATHEMATICS AND COMPUTING↗

Addressing Critical Problems in Materials Science Through Multiscale and Multimode Characterization (Project 1); Characterization and Optimization of Novel Triple-Conducting Oxide Materials for Energy Applications (Project 2) (CRADA Final Report)

PROJECT 1: Address critical problems in materials science and simultaneously advance the state-of-the-art in multiscale and multimode characterization using the combined advanced analytical capabilities and expertise of Colorado School of Mines (CSM) and the National Renewable Energy Laboratory (NREL). The primary effort of the Phase I of this CRADA is to establish the International Center for Multiscale Characterization using shared resources at both NREL and CSM. Phase II will focus on capability development and marketing, choosing candidate materials science issues in the areas of structure imaging, chemical composition mapping, and correlating properties and performance of materials for impact in energy-related, environmental and critical materials areas. The CRADA will be modified to include specific topics of concern in materials science to industry member partners. Advanced analytical capabilities and expertise at CSM and NREL will be used to advance materials understanding and performance through characterization of multiscale phenomena including structural imaging, chemical composition mapping, and other techniques correlating properties and performance of materials. PROJECT 2: As part of the International Center for Materials Characterization, work under Modification #1 will be led by Colorado School of Mines (CSM), working in collaboration with NREL staff to mentor and advise CSM postdoctoral researchers on set up of diffusion annealing experiments. The purpose of the modification is to provide for NREL staff to mentor and advise CSM postdoctoral researchers on set up of diffusion annealing experiments, including mentoring and advising the CSM-NREL team on proper Secondary Ion Mass Spectrometry (SIMS) data analysis as needed. SIMS measurements of 10-20 samples will be performed at NREL during the project duration.

08 HYDROGEN↗

A dynamic variational multiscale method on unstructured meshes for stationary transport problems

Here, this paper presents a variational multiscale (VMS) based finite element method where the stabilization parameter is computed dynamically. The current dynamic procedure takes in a general structure/form of the stabilization parameter with unknown coefficients and computes them dynamically in a local fashion resulting in a dynamic VMS-based finite element method. Thus, a static stabilization parameter with pre-defined coefficients is not needed. A variational Germano identity (VGI) based local procedure suitable for unstructured meshes is developed to perform the dynamic computation in a local fashion. The local VGI based procedure is applied for each interior vertex in the mesh and unknown coefficients are first determined locally at each vertex, and subsequently, for each element a maximum value is taken over the vertices of the element. To make the current procedure practical, a coarser secondary solution is constructed from the primary coarse-scale solution, which is done locally over a patch of elements around each interior vertex. Further, averaging steps are employed to make the local dynamic procedure robust. Currently, the new dynamic VMS formulation is applied to steady problems governed by the advection-diffusion and incompressible Navier-Stokes equations in both 1D and 2D to demonstrate its efficacy and effectiveness.

97 MATHEMATICS AND COMPUTING↗

Application of the NASA Multiscale Analysis Tool: Multiscale Integration and Interoperability

The NASA Multiscale Analysis Tool (NASMAT) was developed recently to allow a wide variety of multiscale analysis problems to be effectively and efficiently solved. The architecture of NASMAT was established specifically to enable parallelized, “plug-and-play” functionality to reduce the complexity associated with adding new features to the code in the future and to allow end users to rapidly implement and evaluate user-defined capabilities. Additionally, the tool utilizes recursive data structures and subroutines to allow for an arbitrary number of length scales when performing multiscale analyses of heterogeneous materials. These features permit the rapid integration of user-defined capabilities (e.g., a material model, micromechanics approach, or failure theory) at all stages within a NASMAT calculation while leveraging built-in techniques where needed. Additionally, these features allow NASMAT to both be called from an external program as well as call an external program. This paper specifically focuses on the multiscale integration and interoperability of NASMAT with other analysis techniques through an illustrative, multiscale analysis of a 3D woven polymer matrix composite (PMC).

NASMAT↗

Multiphysics and Multiscale Simulation Methods for Electromagnetic Energy Assisted Fossil Fuel to Hydrogen Conversion (Final Scientific/Technical Report)

This report summarizes the technical accomplishments of the four-year research project “Multiphysics and Multiscale Simulation Methods for Electromagnetic Energy Assisted Fossil Fuel to Hydrogen Conversion” (Award No. DE-FE0032092), conducted at Howard University and the University of Houston (subawardee) from September 2021 to August 2025. The project successfully achieved all four major objectives: 1. 3D Structural Characterization – Developed 3D optical imaging and mechanical sectioning methods to characterize catalyst distribution and support morphology in nickel foam substrates. Successfully reconstructed 3D geometries and imported them into COMSOL Multiphysics for electromagnetic simulations. 2. EM Hotspot Simulation – Created all-frequency stable electromagnetic formulations and 3D nodal discontinuous Galerkin (NDG) methods for coupled electromagnetic-thermal-fluid problems in multiscale catalytic media. Demonstrated stable solutions from DC to microwave frequencies. 3. Multiphysics Coupling – Developed multiscale simulation methods coupling FEM electromagnetic solvers with thermal transport equations. Reactive molecular dynamics (ReaxFF MD) simulations were performed to investigate catalytic reaction mechanisms at the atomistic level. Demonstrated electromagnetic-thermal co-simulation capabilities for porous catalyst structures. 4. System Optimization – Designed and optimized EM-assisted catalytic systems using nickel foam and carbon foam structures, demonstrating significant temperature increases due to microwave heating. Observed and characterized plasma generation in carbon fiber catalysts. Investigated multiple reaction chamber geometries for improved microwave energy deposition. The project produced significant scientific contributions including 15+ peer-reviewed publications, trained multiple Ph.D. students and undergraduate researchers, and advanced the understanding of microwave-assisted hydrogen production from fossil fuels.

08 HYDROGEN↗

D2NO: Efficient handling of heterogeneous input function spaces with distributed deep neural operators

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. We propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. Here, we demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present three numerical examples to validate its performance.

97 MATHEMATICS AND COMPUTING↗

$\mathrm{IH}$-$\mathrm{GAN}$: A conditional generative model for implicit surface-based inverse design of cellular structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry–property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. Here we further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R 2 -scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.

42 ENGINEERING↗

Comparative investigation of iterative solutions of the all-frequency stable formulation and its vector-potential-only variation

An all-frequency stable formulation has been proposed and applied to solve low-frequency and multiscale electromagnetic problems to avoid the low-frequency breakdown catastrophe of the traditional vector wave equation. Based on the potential representation of the fields, this formulation involves vector and scalar potentials, as well as an auxiliary potential to enforce the gauge condition. In this paper, such a formulation is first simplified to involve vector potential only. Their iterative solutions are then sought by using an incomplete LU preconditioner and an iterative solver. The iterative performance of both formulations are investigated in a comparative study.

Mekonnen, Minyechil↗

Application of the NASA Multiscale Analysis Tool: Multiscale Integration and Interoperability

In order to demonstrate NASMAT’s multiscale operability, a series of illustrative examples will be presented that focus on the application of NASMAT to practical problems. First, the multiscale integration and data recursion is demonstrated by performing a multiscale analysis using only built-in micromechanics methods. NASMAT’s integration is then highlighted by running a multiscale analysis where an external finite element software calls NASMAT. In this case, at each integration point within the finite element model, a local NASMAT analysis is performed to account for failure behavior at the constituent scale. In a similar example, an external program is called from within NASMAT. This case would be relevant for a user wanting to implement an outside micromechanics technique. A combination of these examples is then presented to further illustrate the code’s flexibility when interfacing with outside codes in a multiscale framework. For all examples, data is presented using a custom-developed visualization tool. Additional potential use cases are also addressed. Finally, the plan for upcoming features and added capabilities is discussed.

NASMAT↗

Quantification of Numerical Uncertainty via Nonlinear Dynamical Approach

Motivations (Ensure a Higher Level of Confidence in the Predictability & Reliability of Numerical Simulation for Multiscale Complex Nonlinear Fluid Problems) - The last two decades have been an era when computation is ahead of analysis & when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems & non-traditional fields (Especially when computations offer the ONLY way of generating this type of data limited simulations). - At present some of the numerical uncertainties can be explained and minimized by traditional numerical analysis and standard CFD practices. However, such practices, usually based on linearized analysis, MIGHT NOT be sufficient for strongly nonlinear and/or stiff problems. - We need a good understanding of the nonlinear behavior of numerical schemes being used as an integral part of code verification, validation and certification.

HEC↗

A Partitioned -Task Parallel Implementation of the NASA Multiscale Analysis Tool for High Performance Computing

The NASA Multiscale Analysis Tool (NASMAT) is a “plug and play” software package that allows users to conduct massively multiscale modeling of hierarchical and nonlinear materials. This work extends the scalability and improves the High Performance Computing friendliness of NASMAT by adopting a Partitioned Task-Parallel approach. Interoperability of NASMAT with external software is enhanced through preCICE, a open source library for multiphysics coupling in a partitioned manner. Enhancement through preCICE allows for easy integration of NASMAT to other macro solvers and dissociates the parallelization strategy adopted within NASMAT from the macro solver. The task-parallel framework based on Master-Worker approach is implemented as the parallelization scheme. The scheme accounts for hierarchy of multiple scales (task-dependence) and heterogeneous nature (dynamic load balancing) of computations. The applicability and scalability of the framework will be evaluated by analyzing large scale engineering problems through massively multiscale methods.

NASMAT↗